$B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 6x + 6$ and $ BC = 4x + 22$ Find $AC$.
Solution: A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {6x + 6} = {4x + 22}$ Solve for $x$ $ 2x = 16$ $ x = 8$ Substitute $8$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 6({8}) + 6$ $ BC = 4({8}) + 22$ $ AB = 48 + 6$ $ BC = 32 + 22$ $ AB = 54$ $ BC = 54$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {54} + {54}$ $ AC = 108$